A047617 Numbers that are congruent to {2, 5} mod 8.

2, 5, 10, 13, 18, 21, 26, 29, 34, 37, 42, 45, 50, 53, 58, 61, 66, 69, 74, 77, 82, 85, 90, 93, 98, 101, 106, 109, 114, 117, 122, 125, 130, 133, 138, 141, 146, 149, 154, 157, 162, 165, 170, 173, 178, 181, 186, 189, 194, 197, 202, 205, 210, 213, 218, 221, 226, 229, 234

Offset

1,1

Comments

Numbers whose binary reflected Gray code (A014550) ends with 11. - Amiram Eldar, May 17 2021

Links

Table of n, a(n) for n=1..59.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 8*n - a(n-1) - 9 (with a(1)=2). - Vincenzo Librandi, Aug 06 2010

a(n) = 4*n - (5 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012

G.f.: (2+3*x+3*x^2)/((-1+x)^2*(1+x)). - Harvey P. Dale, Feb 23 2016

a(1)=2, a(2)=5, a(3)=10, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Feb 23 2016

From Franck Maminirina Ramaharo, Jul 22 2018: (Start)

a(n) = A047470(n) + 2.

E.g.f.: (6 - exp(-x) + (8*x - 5)*exp(x))/2. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 - log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021

Mathematica

Select[Range[300], MemberQ[{2, 5}, Mod[#, 8]]&] (* or *) LinearRecurrence[ {1, 1, -1}, {2, 5, 10}, 80] (* Harvey P. Dale, Feb 23 2016 *)

Prog

(Maxima) makelist(4*n -(5 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 22 2018 */
(Python)
def A047617(n): return (n-1<<2)+1+(n&1) # Chai Wah Wu, Mar 30 2024

Crossrefs

Cf. A014550, A047398, A047452, A047461, A047470, A047524, A047535, A047615.

Sequence in context: A003814 A003654 A271787 * A190437 A190249 A188434

Adjacent sequences: A047614 A047615 A047616 * A047618 A047619 A047620

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Aug 06 2010

Status

approved